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```Application Note 20
September 1986
Application Considerations for an
Instrumentation Lowpass Filter
Nello Sevastopoulos
Description
of this, the value of the (R • C) product is critically related
to the ﬁlter passband ﬂatness and to the ﬁlter stability.
The internal circuitry of the LTC1062 is driven by a clock
which also determines the ﬁlter cutoff frequency. For a
maximally ﬂat amplitude response, the clock should be
100 times the desired cutoff frequency and the (R, C)
should be chosen such as:
The LTC®1062 is a versatile, DC accurate, instrumentation
lowpass ﬁlter with gain and phase that closely approximate
a 5th order Butterworth ﬁlter. The LTC1062 is quite different from presently available lowpass switched-capacitor
ﬁlters because it uses an external (R, C) to isolate the
IC from the input signal DC path, thus providing DC accuracy. Figure 1 illustrates the architecture of the circuit.
The output voltage is sensed through an internal buffer,
then applied to an internal switched-capacitor network
which drives the bottom plate of an external capacitor to
form an input-to-output 5th order lowpass ﬁlter. The input
and output appear across an external resistor and the IC
part of the overall ﬁlter handles only the AC path of the
signal. A buffered output is also provided (Figure 1) and
its maximum guaranteed offset voltage over temperature is
20mV. Typically the buffered output offset is 0mV to 5mV
and drift is 1μV/°C. As will be explained later, the use of
an input (R, C) provides other advantages, namely lower
noise and antialiasing.
fC
f
1
≤
≤ C
1.62 2πRC 1.63
where:
fC = ﬁlter cutoff frequency, (–3dB point).
For instance, to make a maximally ﬂat ﬁlter with a –3dB
frequency at 10Hz, we need a 100 • 10Hz = 1kHz internal
or external clock and an external (R, C) such as:
10Hz
1
=
= 6.17Hz
2πRC 1.62
The minimum value of the resistor, R, depends upon the
maximum signal we want to attenuate, and the current
sinking capability of Pin 1 which is typically 1mA. The
10Hz ﬁlter of the previous example should attenuate a
40Hz signal by 60dB. If the instantaneous amplitude of
this signal is 1V peak, the minimum value of the external
resistor should be 1kΩ.
Tuning the LTC1062
Choosing the external (R, C)
In Figure 1, the ﬁlter function is formed by using an external
(R, C) to place the LTC1062 inside an AC loop. Because
R
INPUT
C
FB
1
SWITCHEDCAPACITOR
NETWORK
BOUT
SENSING
OUT
PATH
AGND
s1
2
V–
3
fCLK
OUT
7
V+
6
CLOCK GEN
COSC
÷
4
BUFFERED OUT
8
÷1, 2, 4
OSC
5
AN20 F01
CLOCK
Figure 1. LTC1062 Architecture
an20f
AN20-1
Application Note 20
Figure 2 shows the high accuracy of the passband response
for values of 1/2πRC around (fC/1.62). If maximum ﬂatness
is required, the (R • C) product should be well controlled.
Figures 3 and 4 are similar to Figure 2 but with wider
range of (1/2πRC) values. When the input (R, C) cutoff
frequency approaches the cutoff frequency of the ﬁlter,
the ﬁlter peaks and the circuit may become oscillatory.
This can accidentally happen when using input ceramic
capacitors with strong negative temperature coefﬁcient.
As the temperature increases, the value of the external
capacitor decreases and if the clock driving the LTC1062
stays constant, the resulting (1/2πRC) approaches the
ﬁlter cutoff frequency. On the other hand, if the external
(R • C) has a strong positive temperature coefﬁcient, the
ﬁlter passband at high temperatures will become droopy.
It is important to note that the ﬁlter attenuation slope
is mainly set by the internal LTC1062 circuitry and it is
quasi-independent from the values of the external (R, C).
This is shown in Figure 4, where a 100Hz cutoff frequency
LTC1062 was tested with an external 10kHz clock and for:
7
0.4
1 = fC
2πRC 1.62
PASSBAND GAIN
0
5
4
VOUT/VIN (dB)
0.2
6
1 = fC
2πRC 1.61
1 = fC
2πRC 1.63
–0.2
–0.4
–0.6
–0.8
0.2
0.4
2
Using an external clock: the internal switched-capacitor
network is clock driven and the clock frequency should be
100 times the desired ﬁlter cutoff frequency. Pin 5 of the
LTC1062 is the clock input and an external clock swinging
close to the LTC1062 power supplies will provide the clock
requirements for the internal circuitry. The typical logic
threshold levels of Pin 5 are the following:
VSUPPLY
Vth+
±2.5V
+0.9V
–1V
±5V
+1.3V
–2.1V
±6V
+1.7V
–2.5V
±7V
+1.75V
–2.9V
±8V
+1.95V
–3.3V
±9V
+2.15V
–3.7V
0.6
0.8
1
fIN /fC
10
1 = fC
2πRC 1.13
–10
–20
1
0
–1
–30
–80
0.9
1.0
AN20 F03
Figure 3. Passband Gain vs
Input Frequency
1 = fC
2πRC 3.24
–50
–70
0.8
1 = fC
2πRC 1.94
–40
–60
fC
1
–3 2πRC = 1.78
1 = fC
1 = fC
–4
2πRC 1.94 2πRC 2.11
–5
0.2 0.3 0.4 0.5 0.6 0.7
fIN/fC
1 = fC
2πRC 1.13
1 = fC
2πRC 1.62
0
AN20 F02
Figure 2. Passband Gain vs
Input Frequency
Vth–
The temperature coefﬁcient of the threshold levels is
–1mV/°C.
–2
VS = ±5V
TA = 25°C
fCLK = 100kHz
MYLAR INPUT CAPACITOR
–1.0
0.1
3
1 = fC
2πRC 1.29
1 = fC
2πRC 1.46
1 = fC
2πRC 1.62
LTC1062 Clock Requirements
VOUT/VIN (dB)
fC
f
1
≤
≤ C
3.24 2πRC 1.13
Also, Figure 4 shows that the –30dB/octave slope remains
constant even though the external (R • C) changes.
–90
0.1
VS = ±5V
TA = 25°C
fC = 100Hz
fCLK = 10kHz
1
fIN/fC
10
AN20 F04
Figure 4. Filter Frequency
Response for Various (R, C)
Values and Constant Clock
an20f
AN20-2
Application Note 20
Because the trip levels of Pin 5 are asymmetrically centered
around ground and because (Vth+ – Vth–) is less than the
positive supply voltage, V+, CMOS level clocks operating
from V+ and ground can be AC coupled into Pin 5 and
drive the IC, Figure 5a.
Internal Oscillator
A simple oscillator is internally provided and it is overridden when an external clock is applied to Pin 5. The internal
oscillator can be used for applications for clock requirements below 130kHz and where maximum passband
ﬂatness over a wide temperature range is not required.
The internal oscillator can be tuned for frequencies below
130kHz by connecting an external capacitor, COSC, from
Pin 5 to ground (or negative supply). Under this condition,
the clock frequency can be calculated by:
⎛
33pF
fCLK ≅ 130kHz ⎜
⎝ 33pF + C
OSC
⎞
⎟⎠
(1)
Due to process tolerances, the internal 130kHz frequency
varies and also has a negative temperature coefﬁcient. The
LTC1062 data sheet publishes curves characterizing the
internal oscillator. To tune the frequency of the internal
oscillator to a precise value, it is necessary to adjust the
value of the external capacitor, COSC, or to use a potentiometer in series with the COSC, Figure 5b. The new clock
frequency, f′CLK, can be calculated by:
f′CLK =
fCLK
(1– 4 RCOSC fCLK )
where fCLK is the value of the clock frequency, when R = 0,
from (1). When an external resistor (potentiometer) is
used, the new value of the clock frequency is always higher
than the one calculated in (1). To achieve a wide tuning
range, calculate from (1) the ideal (fCLK, COSC) pair, then
double the value of COSC and use a 50k potentiometer to
Example: To obtain a 1kHz clock frequency, from (1) COSC
typically should be 4250pF. By using 8500pF for COSC and
a 50k potentiometer, the clock frequency can be adjusted
from 500Hz to 3.3kHz as calculated by (2).
The internal oscillator frequency can be measured directly
at Pin 5 by using a low capacitance probe.
Clock Feedthrough
Clock feedthrough is deﬁned as the amount of clock
frequency appearing at the output of the ﬁlter. With ±5V
supplies the measured clock feedthrough was 420μVRMS,
while with ±7.5V supplies it increased to 520μVRMS. The
clock feedthrough can be eliminated by using an (R, C) at
the buffered output, Pin 8, provided that this pin is used
as an output. If an external op amp is used to buffer the
DC accurate output of the LTC1062, an input (R, C) can
be used to eliminate the clock feedthrough, Figure 6, and
to further increase the attenuation ﬂoor of the ﬁlter. Note
that this (R, C) does not really improve the noise ﬂoor of
the circuit since the major noise components are located
near the ﬁlter cutoff frequency.
(2)
VOUT
VIN
1
VOUT
VIN
2
C
V–
V–
1
8
2
7
LTC1062
3
6
4
5
V+
8
LTC1062
7
3
6
4
5
V+
R
0.01μF
V+
AN20 F05b
0
COSC
100k
AN20 F05a
Figure 5a. AC Coupling an External CMOS Clock Powered
from a Single Positive Supply, V+
V–
the Internal Clock Frequency
an20f
AN20-3
Application Note 20
Single 5V Supply Operation
Dynamic Range and Signal/Noise Ratio
Figure 7 shows the LTC1062 operating with a single supply.
The analog ground, Pin 2, as well as the buffer input, Pin 7,
should be biased at 1/2 supply. The value of resistor R1
should conduct 100μA or more. In Figure 7, the resistor
R′ DC biases the buffer and the capacitor C′ isolates the
buffer bias from the DC value of the output. Under these
conditions the external (R, C) should be adjusted such
that (1/2πRC) = fC/1.84. This accounts for the extra AC
There is some confusion with these two terminologies. Because monolithic switched-capacitor ﬁlters are inherently
more noisy than (R, C) active ﬁlters, it is necessary to take
a hard look at the way some IC manufacturers describe
the S/N ratio of their circuit. For instance, when dividing
the ﬁlter’s typical RMS swing by its wideband noise, the
result is called “best case” S/N ratio. But this is deﬁnitely
not “dynamic range”. Under max swing conditions, many
monolithic ﬁlters exhibit high harmonic distortion. This
indicates poor dynamic range even though the S/N ratio
looks great on paper.
The resistor and capacitor (R′, C′) are not needed if the
input voltage has a DC value around 1/2 supply.
If an external capacitor is used to activate the internal oscillator, its bottom plate should be tied to system ground.
–
+
EXTERNAL
BUFFER
C
1
2
V–
VOUT
LTC1050
R1 = 10R
R
VIN
C1 = 0.01C
8
7
LTC1062
3
6
V+
4
5
fCLK
AN20 F06
Figure 6. Adding an External (R1, C1) to Eliminate the Clock
Feedthrough and to Improve the High Frequency Attenuation Floor
R
10μF
SOLID
TANTALUM
+
V+
VIN
C
R1
1
V+/2
8
2
R1
V+
BUFFERED
OUTPUT
6
V+
4
5
CLK
Ra = 12R
Ca
7
LTC1062
3
DC ACCURATE
OUTPUT
AN20 F07
Figure 7. Single Supply Operation
an20f
AN20-4
Application Note 20
With ±5V supplies and higher, the LTC1062 has a typical
100μVRMS wideband noise. With 1VRMS output levels, the
signal/noise ratio is 80dB. The test circuit of Figure 8 is
used to illustrate the harmonic distortion of the device. The
worst-case occurs when the input fundamental frequency
equals 1/2 or 1/3 of the ﬁlter cutoff frequency. This causes
the 2nd or 3rd harmonics of the output to fall into the
ﬁlter’s passband edge, Figures 9a and 9b.
80dB. This is true because the harmonics of the 700Hz
input fall into the ﬁlter’s stopband. With ±7.5V supplies (or
single 15V), the THD of the LTC1062 lies between 76dB
and 83dB, depending on where the harmonics occur with
respect to the circuit’s band edge. A slight improvement,
Figure 9d, can be achieved by increasing the value of the
input resistor, R, such as (1/2πRC) = fC/1.93. Under this
condition, the ﬁlter no longer approximates a max ﬂat
ideal response since it becomes “droopy” above 30% of
its cutoff frequency, as shown in Figure 3.
Figure 9c shows an input frequency of 700Hz and the
ﬁlter’s dynamic range under this condition is in excess of
VIN
1VRMS
(PURE SINE WAVE)
R
26k
C
0.01μF
1
2
–7.5V
0.1μF
7.5V
8
LTC1062
TO SPECTRUM
ANALYZER
7
3
6
4
5
7.5V
0.1μF
AN20 F08
100kHz CLOCK
±5V PEAK-PEAK
Figure 8. 1kHz Cutoff Frequency, 5th Order LP Filter, Test Circuit for Observing Distortion
HORIZ SCALE: 200Hz/DIV
VERT SCALE: 10dB/DIV
fCUTOFF = 1kHz
VIN = 1VRMS AT 500Hz
VS = ±7.5V
HORIZ SCALE: 200Hz/DIV
VERT SCALE: 10dB/DIV
fCUTOFF = 1kHz
VIN = 1VRMS AT 300Hz
VS = ±7.5V
AN20 F09a
AN20 F09b
2ND HARMONIC
FUNDAMENTAL
FUNDAMENTAL
(9a)
3RD HARMONIC
(9b)
HORIZ SCALE: 200Hz/DIV
VERT SCALE: 10dB/DIV
fCUTOFF = 1kHz
VIN = 1VRMS AT 330Hz
VS = ±7.5V
1 = fC
2πRC 1.93
HORIZ SCALE: 500Hz/DIV
VERT SCALE: 10dB/DIV
fCUTOFF = 1kHz
VIN = 1VRMS AT 700Hz
VS = ±7.5V
AN20 F09d
AN20 F09C
3RD HARMONIC = CUTOFF FREQUENCY
CUTOFF FREQUENCY
(9c)
(9d)
Figure 9
an20f
AN20-5
Application Note 20
Step Response and Burst Response
LTC1062 Shows Little Aliasing
The LTC1062 response to an input step approximates
that of an ideal 5th order Butterworth lowpass ﬁlter. Butterworth ﬁlters are “ringy”, Figure 10a, even though their
passband is maximally ﬂat. Figures 10b and 10c show a
more damped step response which can be obtained by
increasing the input (R • C) product and thereby sacriﬁcing
the maximum ﬂatness of the ﬁlter’s amplitude response.
Figures 11a and 11b show the response of the LTC1062
to a 2V peak-to-peak sinewave burst which frequency is
respectively equal to 2 • fC and 4 • fC. It is interesting to
compare Figure 11b to Figure 10a: In both ﬁgures the
overshoots and the settling times are about equal since,
from the ﬁlter’s point of view, a high frequency burst looks
like a step input.
Aliasing is a common phenomenon in sampled data circuits especially when signals approaching the sampling
frequency are applied as inputs. Generally speaking, when
an input signal of frequency (fIN) is applied, an alias frequency equal to (fCLK ± fIN) appears at the ﬁlter’s output.
If fIN is less the (fCLK/2), then the amplitude of the alias
frequency equals the magnitude of fIN multiplied by the
gain of the ﬁlter at fIN, times the (sinx/x) function of the
circuit. For a lowpass ﬁlter, the gain around (fCLK/2) is essentially limited by the attenuation ﬂoor of the ﬁlter and the
(fCLK ± fIN) alias signal is buried into the ﬁlter noise ﬂoor.
The problem arises when the input signal’s frequency is
greater than (fCLK/2) and especially when it approaches
fCLK. Under these conditions (fCLK – fIN) falls either into
200mV/VERT DIV
50ms/HORIZ DIV, fC = 10Hz
5ms/HORIZ DIV, fC = 100Hz
0.5ms/HORIZ DIV, fC = 1kHz
f
1
= C
2πRC 1.94
f
1
= C
2πRC 2.11
f
1
= C
2πRC 1.62
AN20 F10b
AN20 F10a
(10a)
AN20 F10c
(10b)
(10c )
Figure 10. Step Response to a 1V Peak Input Step
TOP TRACE: 0.5V/VERT DIV
TOP TRACE: 0.5V/VERT DIV
100ms/HORIZ DIV, fC = 10Hz
10ms/HORIZ DIV, fC = 100Hz
fIN = 2 s fC
100ms/HORIZ DIV, fC = 10Hz
10ms/HORIZ DIV, fC = 100Hz
fIN = 4 s fC
BOTTOM TRACE: 0.5V/VERT DIV
BOTTOM TRACE: 0.1V/VERT DIV
AN20 F11b
AN20 F11a
(11a)
(11b )
Figure 11. LTC1062 Response to a 2VP-P Sinewave Burst
an20f
AN20-6
Application Note 20
the ﬁlters passband or into the attenuation slope, and then
aliasing occurs. If for instance a 5th order Butterworth
switched-capacitor ladder ﬁlter has a 1kHz corner frequency
and operates with a 50kHz clock, a 49kHz, 1VRMS input
signal will cause an alias (1kHz, 0.7VRMS) signal to appear
at the output of the circuit; a 48kHz input will appear as a
2kHz output attenuated by 30dB.
Two LTC1062s can be cascaded with or without intermediate buffers. Figure 12 shows a DC accurate 10th order
lowpass ﬁlter where the second LTC1062 input is taken
directly from the DC accurate output of the ﬁrst one.
passband error, the second resistor, R′ should be much
larger than R. The recommended ratio of (R′/R) is about
117/1; beyond this, the passband error improvement is
not worth the large value of R′. Also, under this condition
(1/2πRC) = fC/1.57 and (1/2πR′C′) = fC/1.6. For instance,
a 10th order ﬁlter was designed with a cutoff frequency,
fC, of 4.16kHz, fCLK = 416kHz and R = 909Ω, R′ = 107k,
C = 0.066μF and C′ = 574pF. The maximum passband
error was –0.6dB occurring around 0.5 • fC. Figure 13
repeats the circuit of the previous ﬁgure but the second
LTC1062 is fed from the buffered output of the ﬁrst one.
The ﬁlter’s offset is the offset of the ﬁrst LTC1062 buffer
(which is typically under ±5mV and guaranteed 20mV
over the full temperature range of the device). By using
The LTC1062 internal circuitry has a 4th order sampled
data network so, in theory, it will be subject to the above
aliasing phenomenon. In practice, however, the input (R, C)
band limits the incoming, clock-approaching signals, and
aliasing is nearly eliminated. Experimental work shows
the following data:
STANDARD 6th ORDER
LTC1062
SWITCHED CAPACITOR LOWPASS
fIN, 0dB LEVEL VOUT AT (fCLK – fIN)
FILTER VOUT AT (fCLK – fIN)
–77dB
–22.0dB
0.97 • fCLK
0.98 • fCLK
–64dB
–3.5dB
0.99 • fCLK
–43dB
0dB
0.995 • fCLK
–45dB
0dB
0.999 • fCLK
–60dB
0dB
Ra
R
DC ACCURATE OUTPUT
VIN
C
V–
Ca
1
8
1
8
2
7
2
7
LTC1062
3
6
4
5
V–
LTC1062
3
6
4
5
BUFFERED OUTPUT
AN20 F12
V+
fCLK
Ra
R
VOUT
VIN
C
–5V
Ca
1
8
1
8
2
7
2
7
LTC1062
3
6
4
5
–5V
LTC1062
3
6
4
5
BUFFERED OUTPUT
AN20 F13
V+
fCLK
Figure 13. Cascading Two LTC1062s. The 2nd Stage is
Driven by the Buffered Output of the First Stage
an20f
AN20-7
Application Note 20
this intermediate buffer, impedance scaling is no longer
required and the values of R and R′ can be similar. With
this approach the passband gain error is reduced to
–0.2dB. The recommended equation of the two (R, C)
s are the following: (1/2πRC) = fC/1.59 and (1/2πR′C′) =
fC/1.64 or vice versa.
of the ﬁlter was 140μVRMS and the worst-case second
harmonic distortion occurred with fIN = 0.5 • fC as shown
in Figure 14. With 1VRMS input levels, the signal-to-noise
ratio is 77dB and the worst-case dynamic range is 73dB.
Figure 15 illustrates a 12th order ﬁlter using two LTC1062s
and a precision dual op amp. The ﬁrst op amp is used as
a precision buffer and the second op amp is used as a
simple 2nd order noninverting lowpass ﬁlter to provide the
remaining two poles and to eliminate any clock noise.
A 4kHz lowpass ﬁlter was tested with the circuit of Figure 13.
The measured component values were R = 97.6k and
C = 676pF, R′ = 124k and C′ = 508pF. The wideband noise
VERT SCALE: –10dB/DIV
HORIZ SCALE: 500Hz/DIV
AN20 F09d
2ND HARMONIC = CUTOFF FREQUENCY
Figure 14. Response of the Filter of Figure 13 to a 2kHz
1VRMS Input Sinewave. The 2nd Harmonic (Worst Case)
Occurs at the Filter’s Cutoff Frequency
–
–
Ra
1/2 LTC1051
+
1/2 LTC1051
R
+
VIN
Ca
1
2
VOUT
C2
C
V–
R1
C1
R2
1
8
LTC1062
2
7
3
6
4
5
V–
8
LTC1062
7
3
6
V+
4
5
fCLK
AN20 F15
Figure 15. A Very Low Offset, 12th Order, Max Flat Lowpass Filter
R = 59k, C = 0.001μF, R1 = 5.7k, C1 = 0.01μF
R1 = R2 = 39.8k, C1 = 2000pF, C2 = 500pF, fCLK = 438kHz, fC = 4kHz
an20f
AN20-8
Application Note 20
The output ﬁlter is tuned at the cutoff frequency of the
LTC1062s and has a Q = 1 to improve the passband error
around the cutoff frequency. For gain and Q equal to unity,
the design equation for the center frequency, fO, is simple:
let C1/4C2 and R1 = R2, then fO = 1/(πR1C1). The ﬁlter’s
overall frequency response is shown in Figure 16 with a
438kHz clock. The measured DC output offset of the ﬁlter
was 100μV, although the maximum guaranteed offset of
each op amp over temperature would be 400μV. Because
the active (R, C) output ﬁlter is driven directly from the
DC accurate output of the second LTC1062, impedance
scaling is used with the resistor R′. The noise and distortion performance of this circuit is very similar to the one
described for Figure 13.
should be limited well below half the clock frequency;
otherwise, aliasing will severely limit the ﬁlter’s dynamic
range.
The LTC1062 can be used to create a notch because the
frequency where it exhibits –180° phase shift is inside its
passband as shown in Figure 17. It is repeatable and predictable from part to part. An input signal can be summed
with the output of the LTC1062 to form a notch as shown
in Figure 18. The 180° phase shift of the LTC1062 occurs
at fCLK/118.3 or 0.85 times the lowpass cutoff frequency.
For instance, to obtain a 60Hz notch, the clock frequency
should be 7.098kHz and the input 1/(2πRC) should be
approximately 70.98Hz/1.63. The optional (R2C2) at the
output of the LTC1062 ﬁlters the clock feedthrough. The
1/(2πR2C2) should be 12 to 15 times the notch frequency.
The major advantage of this notch is its wide bandwidth.
The input frequency range is not limited by the clock
frequency because the LTC1062 by itself does not alias.
Using the LTC1062 to Create a Notch
Filters with notches are generally difﬁcult to design and
they require tuning. Universal switched-capacitor ﬁlters
can make very precise notches, but their useful bandwidth
0
fCLK = 438kHz
VIN = 1VRMS
VS = ±5V
VOUT PHASE SHIFT (DEGREES)
0
–20
VOUT/VIN (dB)
–20
–40
–60
–80
–100
–40
1 = fC
2πRC 1.62
–60
–80
–100
–120
–140
1 = fC
2πRC 1.94
1 = fC
2πRC 1.78
–160
1 = fC
2πRC 1.62
–180
–200
1 = fC
2πRC 1.78
–220
–240
1
10
fIN (kHz)
100
0.2
0.3
0.4
0.5
0.6 0.7
fIN/fC
AN20 F16
0.8
0.9
1.0
AN20 F17
Figure 16. Frequency Response of the
12th Order Filter of Figure 15
Figure 17. Phase Response of the LTC1062
for Various Input (R, C)s
R1
R4
VIN
R
R2
C
V–
R3
–
C2
1
8
2
7
LTC1062
+
VOUT
LT®1056
OPTIONAL
3
6
V+
4
5
CLK IN
fCLK = fnotcht
1 G
notch
2πRC
AND R1 = R4 = (R2 + R3)
AN20 F18
Figure 18. Using the LTC1062 to Create a Notch
an20f
AN20-9
Application Note 20
The frequency response of the notch circuit is shown in
Figure 19 for a 25Hz notch. From part to part, the notch
depth varies from 32dB to 50dB but it can be optimized
by tuning resistor R1. Figure 20 shows an example of the
wideband operation of the circuit. These pictures were
taken with the ﬁlter operating with a 3kHz clock frequency
and forming a 25Hz notch. Figure 20a shows the circuit’s
response to an input 1kHz, 1VRMS sinewave; Figure 20b
shows the response to a 10kHz, 1VRMS sinewave. The high
frequency distortion of the ﬁlter will depend on the quality
of the external op amp and not on the ﬁlter. The measured
wideband noise from DC to 20kHz was 138VRMS and the
measured noise from 50Hz to 20kHz was 30μVRMS.
The circuit of Figure 21 is an extension of the previous
notch ﬁlter. The input signal is summed with the lowpass
ﬁlter output through A1, as previously described; then,
the output of A1 is again summed with the input voltage
through A2.
VERT SCALE: 10dB/DIV
HORIZ SCALE: 1kHz/DIV
10
AN20 F20a
fCLK = 2957Hz
0
fCLK = 3kHz
fIN = (1kHz, 1VRMS)
VOUT, VIN (dB)
–10
(20a) Response of a 25Hz Notch Filter to a 1kHz,
1VRMS Input Sinewave
–20
–30
–40
–50
–60
VERT SCALE: 10dB/DIV
HORIZ SCALE: 5kHz/DIV
–70
10
1k
100
10k
fnotch
100k
fCLK
fIN (Hz)
AN20 F19
Figure 19
AN20 F20b
fIN = (10kHz, 1VRMS)
fCLK = 3kHz
(20b) Same as Above but the Input is a 10kHz Sinewave
Figure 20
C7
0.1μF
R6
19.35k
R3
20k
R4
10k
R7
20k
R = 9.09k
VIN
C
1μF
R2
20k
1
2
V–
3
4
8
LTC1062
A1
1/2 LT1013
7
6
5
–
V+
R5
10k
+
CLK IN
2.84kHz
1 = fCLK
2πRC t
–
A2
1/2 LT1013
+
VOUT
AN20 F21
Figure 21. A Lowpass Filter with a 60Hz Notch
an20f
AN20-10
Application Note 20
5.23k
VIN
VOUT
+
10μF
10μF
+
If R6 = R2 = R3 = R7 and R4 = R5 = 0.5R7, the output
of A2 at least theoretically, should look like the output of
LTC1062 Pin 8. If the ratio of (R6/R5) is slightly less than
2, a notch is introduced in the stopband of the LTC1062
as shown in Figure 22. The overall ﬁlter response looks
pseudoelliptic lowpass. The frequency of the notch is at
fCLK/47.3 and the value of the resistor ratio (R6/R5) should
be equal to 1.935.
1
8
2
–5V
B.VOUT
7
LTC1062
3
6
4
5
5V
0.08μF
AN20 F23
Figure 23. A Low Frequency, 5Hz Filter Using
Back to Back Solid Tantalum Capacitors
0
VOUT/VIN (Hz)
10
20
Clock Circuits
30
Application Note 12 describes in detail various clock
generation techniques which can be applied for the
LTC1062 requirements. Two basic circuits are repeated
and explained below:
40
50
60
70
1
10
60 100
fIN (Hz)
1000
AN20 F22
Figure 22. Amplitude Response of the Filter, Figure 21
Experimental work, done in a laboratory environment,
shows that the passband gain error is the same when
mylar, polystyrene and polypropylene capacitors are used.
All the experiments done for this application note used
mylar capacitors for 0.001μF and up and silver mica for
less then 1000pF.
Solid tantalum capacitors connected back to back, as
shown in Figure 23, introduce an additional passband error of 0.05dB to 0.1dB. For cutoff frequencies well below
10Hz and for limited temperature range , the back to back
solid tantalum capacitor approach offers an economical
and board saving solution provided that their leakage and
tolerances are acceptable. When disc ceramic capacitors were used as part of the required input (R, C) of the
LTC1062, the passband accuracy of the ﬁlter was similar
to that obtained with solid tantalum capacitors. Ceramic
capacitors should be avoided primarily because of their
large and unpredictable temperature coefﬁcient. NPO
ceramic capacitors, however, are highly recommended
especially for military temperature range. Their maximum
available value is of the order of 0.1μF, their physical size is
reasonable and they are available with ±20ppm/°C tempco.
1. Low frequency oscillators: A simple (R, C) oscillator is
shown in Figure 24. It uses a medium speed comparator with hysteresis and a feedback (R1, C1) as timing
elements. The capacitor, C1, charges and discharges
to 2V+/3 and V+/3 respectively. Because of this, the
frequency of oscillation is, at least theoretically, independent from the power supply voltage. If the comparator
swings to the supply rails, if the pull-up resistor is much
smaller than the resistors Rh and if the propagation
delay is negligible compared to the RC time constant,
the oscillation frequency is:
fOSC =
0.72
R1C1
R1
V+
3
2.74k
8
+
7
LT1011
100k
2
OUT
4
–
1
C1
100k
100k
AN20 F24
Figure 24. A Low Frequency, Precision (R, C) Oscillator. For
Bipolar ±5V Output Swing Refer the Ground Connection to –5V
an20f
Information furnished by Linear Technology Corporation is believed to be accurate and reliable.
However, no responsibility is assumed for its use. Linear Technology Corporation makes no representation that the interconnection of its circuits as described herein will not infringe on existing patent rights.
AN20-11
Application Note 20
For LT111 or LT1011 type comparators, this holds for
fOSC ≤ 3kHz. The circuit of Figure 24 is adequate to drive
an LTC1062 tuned in the vicinity of 10Hz to 30Hz cutoff
frequency. Also, when the input (R, C) of the LTC1062
and the (R1, C1) of the comparator have the same
temperature coefﬁcient, the cutoff frequency will drift
but the passband error will be temperature independent
since:
f
0.72
1
≅ C =
or (R1C1/ RC) = 1/ 36
2πRC 1.63 163 •R1C1
For C = 10C1, then R = 3.6R1, which yields a reasonable
gates as active elements, Figure 26. Their frequency,
however, is usually above 1MHz and should be divided
down before being applied to the LTC1062. Figure 27
shows an inexpensive discrete crystal oscillator using a
single transistor as gain element. Its output can directly
drive Pin 5 of the LTC1062 and its Pin 4, should they
be converted to analog ground or negative supply to
activate the internal divide by 2 or 4 of the circuit. This
is necessary because the duty cycle at the collector of
the crystal oscillator is not 50%.
100kHz
1k
3k
74LS04
1200pF
74LS04
2M
2. The RC oscillator of Figure 24 can also be used up to
110kHz but the frequency of oscillation is about equal
to 0.66/R1C1 and the duty cycle 60%. Again the major
frequency drift component will be due to the drift of
the R1C1. If the cutoff frequency of the ﬁlter should
be made as temperature independent as possible, the
(R • C) and (R1 • C1) products should also be made
temperature independent. This can be achieved by
choosing resistors and capacitors of nearly opposite
temperature coefﬁcients. For instance, TRW MTR-5/
+ 120ppm/°C resistors can be used with –120ppm/°C
±30ppm WESCO type 32-P capacitors.
OUT
74C14
43pF
1k
74LS04
68pF
6.8M
0.25μF
1k
68pF
1MHz
OUT
4049
68pF
10MHz
OUT
68pF
68pF
68pF
AN20 F26
3. Crystal oscillators: Figure 25 shows an LT1011 comparator biased in its linear mode and using a crystal to
establish its resonant frequency. With this circuit we can
achieve a few hundred kHz, temperature independent
clock frequency with nearly 50% duty cycle. Many
systems already have a crystal oscillator using digital
Figure 26. Typical Gate Oscillators
V+ = 5V
2k
2k
TO LTC1062
PIN 5
33k
V + = 5V
2N3904
1N4148
1pF
5MHz
OUT
2k
C1
C2
fCRYSTAL
C1
C2
3.58MHz 150pF 150pF
1MHz 150pF 680pF
400kHz 390pF 2000pF
1N4148
100k
AN20 F27
–5V
400k
2
7
LT1011
100k
3
680pF
Figure 27. Discrete, Low Cost Oscillator
Using Parallel Type AT-CUT Crystal
8
+
OUT
4
–
Acknowledgement
25k
1
For this application note, the laboratory work was done
by Guy Hoover whose meticulousness and contributions
are greatly appreciated.
AN20 F25
V – = –5V
Figure 25. Crystal Oscillator with 50% Duty Cycle
an20f
AN20-12
Linear Technology Corporation
IM/GP 986 10K • PRINTED IN USA
1630 McCarthy Blvd., Milpitas, CA 95035-7417
(408) 432-1900 ● FAX: (408) 434-0507
●
www.linear.com
```
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